As is well known, the boundary of the geometry bends inward toward the horizons by an amount that depends on the temperature [1]}. For very low \(T\)  the boundaries bend in very little and the distance between them at \(t=0\)  is large as in the left panel. But as the temperature increases the boundaries move closer to the horizon and if one follows the formulas to \(T \rightarrow \infty \)  (or tomperature to \({\cal {J}}\) ) they get within a cutoff distance
\({{\cal {J}}}^{-1}\)  of the horizons as in the right panel. In the high temperature limit the boundary merges with the stretched horizon and the holographic degrees of freedom cannot be distinguished from horizon modes. To put it another way, the boundary degrees of freedom become the quasinormal horizon modes.
